Multidimensional process window optimization in semiconductor manufacturing

ABSTRACT

A method for optimizing multiple process windows in a semiconductor manufacturing process is disclosed. The message comprises performing dependent variable composition on a plurality of dependent variables. Metrology data is joined with the dependent variables, and then a partial least squares regression is performed on the joined data set to obtain a prediction equation, and a variable importance prediction for each process window in a process window set. A set of product limited yield are derived, and the process window set is adjusted, and the yields recalculated, until an optimal process window set is derived.

FIELD OF THE INVENTION

This invention relates generally to semiconductor device fabrication,and more particularly to techniques for optimizing process windows usedduring the fabrication process.

BACKGROUND OF THE INVENTION

In semiconductor design, particularly SRAM design, it is often desirableto create a contact bridge between contacts in very close proximity. Inparticular, contact areas (CAs) are connected together to form complexcircuits from basic transistors. For example, the gate of one transistormay be connected to the drain or source of another transistor.

Modern semiconductor devices typically have multiple levels of metalinterconnects. The metal interconnects are typically formed via adeposition and patterning sequence as is known in the art. During theprocess of forming interconnects, defects, such as CA opens and CAshorts decrease the overall production yield. Various parameters affectthe probabilities of CA opens and CA shorts. Moving a process window inone direction may reduce the number of CA opens, but increase the numberof CA shorts. There is an inherent tradeoff in semiconductormanufacturing between the number of CA shorts and the number of CAopens.

In current semiconductor fabrication techniques, a process window isoptimized for only one parameter at a time, and the tradeoff between CAopens and CA shorts is not well accounted for. For example, if a CD(critical dimension) process window is optimized, this will require ashift in the oxide thickness process window. However, if the oxidethickness process window is to be optimized, the CD process window willthen shift. This can adversely affect the overall production yield.Therefore, what is desired is a technique for improved process windowoptimization, which will in turn improve overall production yields insemiconductor manufacturing.

SUMMARY OF THE INVENTION

The present invention provides a method for optimizing multiple processwindows, each process window corresponding to a different parameter, ina semiconductor manufacturing process, comprising the steps of:

performing dependent variable composition on a plurality of dependentvariables;retrieving metrology data for each process parameter;joining the plurality of dependent variables and the metrology data toform a joined data set;performing a partial least squares regression on the joined data set toobtain a prediction equation, and a variable importance prediction foreach process parameter;generating a process target value for each parameter, based on the valueof the corresponding variable importance prediction;generating a new process window for each parameter, based on thecorresponding process target value, thereby forming a process windowset; andevaluating the process window set by deriving a plurality of productlimited yield values based on data corresponding to the process windowset, and comparing it to the plurality of product limited yield valuesderived with a previous process window set, and computing a predictedproduct yield value based on the product of the plurality of productlimited yield values; whereby the steps of generating a process targetvalue for each parameter, based on the value of the correspondingvariable importance prediction and generating a new process targetwindow for each parameter, based on the corresponding process targetvalue are repeated until the predicted product yield value has reachedan optimal value, thereby deriving an optimized process window set.

Additionally, the present invention provides a method that furthercomprises the step of generating a report displaying the process targetvalue corresponding to each process window of the optimized processwindow set.

Additionally, the present invention provides a method that furthercomprises the step of generating a report displaying the process lowerspecification limit, and upper specification limit corresponding to eachprocess window of the optimized process window set.

Additionally, the present invention provides a method that furthercomprises the step of inputting the optimized process window set to oneor more process tools.

Additionally, the present invention provides a method in which the stepof evaluating the process window set by deriving a plurality of productlimited yield values comprises deriving a CA open product limited yield,and deriving a CA short product limited yield.

Additionally, the present invention provides a method in which theplurality of dependent variables are selected from the group consistingof:

oxide thickness before contact lithography;contact size after lithographic development; contact etch bias; andcontact-to-polysilicon alignment.

Additionally, the present invention provides a method in which the stepof performing dependent variable composition comprises the steps of:

measuring a test structure yield for each dependent variable on aplurality of semiconductor devices;calculating a lambda value based on the measured test structure yield;deriving a product limited yield for each dependent variable based onthe lambda value;multiplying each product limited yield together to derive a predictedproduct yield.

Additionally, the present invention provides a method that furthercomprises the steps of: generating a plurality of bucket indices,wherein each bucket index corresponds to a process window, and eachprocess window overlaps with the process window of at least one adjacentbucket index; and

in which the step evaluating the process window set by deriving aprocess yield value based on data corresponding to the process windowset comprises inputting bucket observation values into the predictionequation.

Additionally, the present invention provides a method that furthercomprises the step of generating a yield response curve based on theoptimized process window set.

Additionally, the present invention provides a method in which the stepof generating a plurality of bucket indices comprises generating atleast six bucket indices.

Additionally, the present invention provides a method in which the stepof generating a plurality of bucket indices comprises generating bucketindices corresponding to buckets comprising process windows that overlapwith the process window of at least one adjacent bucket.

Additionally, the present invention provides a system for optimizingmultiple process windows, comprising:

a data collection module;a regression module;a computation module; anda report module, in which the data collection module is configured toaggregate metrology data and input data, and communicate the metrologydata and input data to the regression module, the regression moduleconfigured to perform a partial least squares regression, and compute atleast one variable importance prediction, and a prediction equation, theregression module further configured to communicate the at least onevariable importance prediction, and the prediction equation to thecomputation module, the computation module configured to compute one ormore optimal process windows, product limited yields, and predictedproduct yields, the computation module further configured to communicatethe optimal process windows, product limited yields, and predictedproduct yields to the report module, the report module configured tooutput at least one report

Additionally, the present invention provides a system in which thereport module is configured to output a report in a tabular format, thereport indicating values for a target value corresponding to eachoptimal process window.

Additionally, the present invention provides a system in which thereport module is further configured to output a report indicating valuesfor a lower specification limit, and an upper specification limitcorresponding to each optimal process window.

Additionally, the present invention provides a system in which thereport module is configured to output a report in a graphical format,the report comprising a yield response curve superimposed on a bar graphrepresentative of a distribution of observed values of a processparameter

Additionally, the present invention provides a system in which thecomputation module is configured to generate a plurality of bucketindices, wherein each bucket index corresponds to a process window, andeach process window overlaps with the process window of at least oneadjacent bucket index

Additionally, the present invention provides a system that furthercomprises a tool configuration module, wherein the tool configurationmodule is configured to receive process windows form the computationmodule, and wherein the tool configuration module is configured tocommunicate process windows to one or more process tools.

Additionally, the present invention provides a system in which theprocess tool comprises an etch tool.

Additionally, the present invention provides a system in which theprocess tool comprises a deposition tool.

Additionally, the present invention provides a system in which theprocess tool comprises a lithography tool.

BRIEF DESCRIPTION OF THE DRAWINGS

The structure, operation, and advantages of the present invention willbecome further apparent upon consideration of the following descriptiontaken in conjunction with the accompanying figures (FIGs.). The figuresare intended to be illustrative, not limiting.

In the drawings accompanying the description that follows, often bothreference numerals and legends (labels, text descriptions) may be usedto identify elements. If legends are provided, they are intended merelyas an aid to the reader, and should not in any way be interpreted aslimiting. Note that this disclosure contains various charts and graphsthat contain numbers. To aid in distinguishing reference numbers fromnumbers that are part of the chart legends, an “Arial” font is used forchart legends, and an italicized “Times Roman” font is used forreference numbers.

FIG. 1 is a graph showing a yield response curve for CA open defects.

FIG. 2 is a graph showing a yield response curve for CA short defects.

FIG. 3 is a graphical representation of the effects of interaction ofprocess windows on product yield.

FIG. 4 is a flowchart indicating process steps to perform the method ofthe present invention.

FIG. 5 is a graph showing a yield response curve for overall productyield derived using prior art methods.

FIG. 6 is a graph showing a yield response curve for overall productyield derived using the method of the present invention.

FIG. 7 is a chart showing the relationship between bucket numbers andprocess windows.

FIG. 8 is a flowchart indicating process steps to perform an alternativeembodiment of the method of the present invention.

FIG. 9 shows a block diagram 900 of an exemplary system that implementsthe present invention.

DETAILED DESCRIPTION OF THE INVENTION

In the description that follows, numerous details are set forth in orderto provide a thorough understanding of the present invention. It will beappreciated by those skilled in the art that variations of thesespecific details are possible while still achieving the results of thepresent invention. Well-known processing steps and materials aregenerally not described in detail in order to avoid unnecessarilyobfuscating the description of the present invention.

FIG. 1 is a graph showing a yield response curve 102 for CA opendefects. The yield response curve 102 represents the yield ofsemiconductor devices as a function of an arbitrary process parameter,indicated on the X axis as Parameter A. The graph of FIG. 1 is adual-Y-axis graph. The right Y axis is labeled “yield” and representsthe percent yield, due only to CA open defects (referred to as the CAopen yield), as graphically indicated by yield response curve 102. Theyield response curve 102 is superimposed on a bar graph comprising aplurality of bars 104.

The bars on the graph (indicated generally as 104) represent adistribution of the number of observed values of parameter A duringempirical observations. Each bar 104 represents a distinct range ofvalues for parameter A. For example, the bar at the X axis point of 0.08represents approximately 9800 observations with parameter A in the rangeof 0.075-0.085. The left Y axis is labeled “numobs” to signify the“number of observations” of parameter A that fell into a particularrange during a processing step of semiconductor manufacturing (such as,a metallization or etch step, for example). As indicated by responsecurve 102, the CA open yield increases as the value of parameter Aincreases.

FIG. 2 shows a similar chart as FIG. 1, but for the CA short yield, as afunction of parameter A. In this case, the CA short yield response curve106 indicates that the CA short yield (i.e. the yield due only to CAshort defects) decreases as the value of parameter A increases. Hence,there is a tradeoff in deciding the optimal value of parameter A. Ifparameter A is too low, then the CA open yield will be poor, making theoverall yield poor. If parameter A is too high, then the CA open yieldwill improve, but the CA short yield will be low, and overall yield willtherefore below. Therefore it is desirable to pick the optimal value ofparameter A to optimize overall yield.

However, in practice, semiconductor processes are typically subject tomultiple parameters, that may have interdependence among each other.Hence, for effective process optimization, it is necessary to identifywhich parameters are the most significant in determining the yield of aprocess, and then to determine where the optimal range of values(process window) for each parameter. Furthermore, it is desirable tomake this determination as early as possible in the semiconductormanufacturing process. The present invention allows this assessment tobe made during an intermediate metallization process, therefore allowingoptimizations to be made earlier, rather than later.

FIG. 3 shows a chart providing a graphical representation of interactionamongst two parameters. In this case, parameter A is on the X axis ofthe chart. Parameter B is on the Y axis of the chart. Three regions onthe chart indicate three different overall product yield percentages. Inthis exemplary dataset, region 112 represents a yield of 89.06 percent,region 114 represents a yield of 79.69 percent, and region 116represents a yield of 84.38 percent. If the value of parameter A exceeds0.080, then the value of parameter B has an impact on product yield. Asis shown in the chart, if the value of parameter A exceeds 0.080, thenif the value of parameter B exceeds 3,550, the resulting product yield(represented by region 114) is 79.69 percent. Similarly, if the value ofparameter B is below 3,550, then the resulting product yield(represented by region 116) is 84.38 percent.

However, if the value of parameter A is kept below 0.080, then theeffect of parameter B becomes negligible on product yield. In this case(represented by region 112), product yield is 89.06 percent, and thereis no need to include parameter B in the optimization process.

FIG. 4 is a flowchart 400 indicating process steps to perform the methodof the present invention. In practice, these steps are performed viasoftware executing on a computer system. In process step 420, thevarious dependent variable data is loaded into the computer system, in aformat able to be read by the software executing the method of thepresent invention, such as a database, flat file, or other structuresuitable for this purpose. In step 422, dependent variable compositionis performed. In this step, the product limited yield (“limited yield”is a terminology in semiconductor manufacturing referring to the yieldrelated to one mechanism, such as CA opens) is computed as a function ofthe yield of the corresponding test structure. The use of such teststructures are standard industry practice.

In the case of CA opens and CA shorts, the following formulas are used:

Product limited yield(CA open)=f(test structure yield of CA open)Productlimited yield(CA short)=f(test structure yield of CA short)The predictedproduct yield(the overall yield for the product)is then performed bycomputing the product of all the product limited yields.

Predicted Product yield(combined CA short and CA open)=Product limitedyield(CA open)*Product limited yield(CA short)

The functions to derive the product limited yields from the teststructure observations can be based on the negative binomial yieldmodel. In this case the test structure yield TSy (for CA open) is:

TSy(CA Open)=1/(1+lambda*N1/alpha)̂alpha

Where alpha is a clustering factor (a measure of the positionalcorrelation between separate defects) based on actual data, N1 is thenumber of contacts in test structure, and lambda is the fail rate ofcontact opens. Since all variables except lambda are known a priori,lambda can be solved by this equation.

The product limited yield PLy(CA open) is then calculated as

PLy(CA open)=1/(1+lambda*N2/alpha)̂alpha

Where N2 is the number of contacts in the product, and the lambda valueis previously derived from the test structure observations. A similarapproach is used to derive predicted yields for CA short defects. Notethat if there is only one dependent variable to be considered (e.g. onlyCA open yield), then the method can proceed directly from process step420 to step 424, without going to process step 422.

In process step 424, metrology data pertaining to the actual test run ofthe fabrication process are retrieved from the corresponding processtools (e.g. etch tools, lithographic tools, furnaces, for example).

In process step 426, the input data is combined with the metrology dataused during the fabrication process. This process step pairs observed orcomposed product yield results with a corresponding set of processwindows. This collection of data is referred to as a joined data set. Atthis point in the method, the various dependent variables (CA open yieldand CA short yield) and the corresponding process windows (e.g.parameter A, and parameter B) are available for regression analysis inprocess step 428.

In process step 428, a partial least squares regression technique isperformed on the data that is aggregated in process step 426. Thepartial least squares regression is a well-known mathematical techniquethat can be performed by a variety of commercial software packages, suchas Statistics Toolbox, by MathWorks, of Natick Mass., and XLSTAT-PLS, byKovach Computing Services, of Wales, U.K., just to name a few.

The partial least squares regression is useful for balancing the twoobjectives of explaining response variation and explaining predictorvariation. In the present invention the partial least squares regression(PLS) is used for cross validation.

Part of this process involves selecting the number of parameters used tofit the model to only part of the available data (the training set) andto measure how well models with different numbers of extracted factorsfit the other part of the data (the test set). These selected parametersare called predictors, and this technique is called test set validation.

However, for semiconductor manufacturing processes, it is not usuallyfeasible to obtain sufficient data to make both parts large enough forpure test set validation to be useful. Therefore, the present inventionemploys the technique of performing several different divisions of theobserved data into training sets and test sets. This is called crossvalidation.

As a result of the PLS regression, a Variable Importance Prediction(VIP) value is produced for each predictor, as well as a predictionequation that predicts product yield based on the values of thepredictors. The VIP represents the significance of each selected processparameter (predictor) in determining the product yield. If a predictorhas a relatively small coefficient (in absolute value) and a small valueof VIP, then it is a prime candidate for deletion (e.g. not beingconsidered in the optimization process).

The significance of each predictor is ranked, based on the absolutevalue of VIP, with a larger absolute value indicated more significance.The sign of the value of the VIP determines the direction to move theprocess window target in order to positively affect the process yield.If the sign of the VIP value is positive, it means that by shifting theprocess window of the corresponding predictor (e.g. process A) to theright, process yield will improve. If the sign is negative, shifting theprocess window to left will improve process yield.

The derived VIP values for each predictor (e.g. parameter A, parameterB, etc. . . . ) are used to derive a new process target set in processstep 430. This involves selecting a new set of ideal values for theparameters.

From the process target set, a new process window set is generated inprocess step 432. In this case, each target value is used to define arange. For example, the achievable process range for parameter A may beplus or minus 0.010. Therefore, if the target value for parameter A is0.080, then process window for parameter A is 0.070-0.090. As theparameter A target value is adjusted, the process window for parameter Ais adjusted accordingly.

In process step 434, the new process window set is evaluated by usingthe product yield formulas described earlier and determining if the newprocess window set is an improvement over the previous process windowset. If the new process window set improves yield, then a new processtarget set is created by adjusting the target values of each parameter.The adjustments are made by predetermined increments. For example, thenext iteration may shift the target value for parameter A to 0.082, andthen to 0.084, and so on, each time repeating the analysis. If thepredicted yield is improved, then the process targets are adjustedagain, in process step 436, and then process steps 432 and 434 arerepeated until no further improvement in yield is predicted. At thatpoint the optimized process window set is output to a report in processstep 438.

For example, suppose a fabrication process has two process parameters,A, and B. Furthermore, suppose that parameter A has a higher VIPabsolute value than parameter B. In this case, for step 432, parameter Ais adjusted first, and an operating range for parameter A about theoptimal value defines a first process window for parameter A. Next,parameter B is adjusted until the product yield is optimal, and a rangebased on that optimal value forms the first process window for parameterB. The combination of process window A and process window B comprise afirst process set. The product yield for the first process set isevaluated in step 434. This evaluation is based on the product yieldformulas described earlier. In step 436, the process window forparameter A is shifted, and the procedure repeats, with a new processwindow for parameter B being generated. This forms a second processwindow set. The first and second process window sets are compared. Theprocedure repeats until an optimal process window set is obtained.

FIG. 5 is a graph showing a yield response curve 502 as a function ofparameter B, for overall product yield derived using prior art methods.As can be seen, yield response curve 502 has multiple peaks within theprocess window range. This makes it difficult to locate the optimalprocess yield within the achievable limits of the process window forparameter B.

FIG. 6 is a graph showing a yield response curve 602 for overall productyield derived using the method of the present invention. Note that the Xaxis in FIG. 6 is a bucket index, as compared with the X axis of FIG. 5,which is parameter B. The bucket index is a synthesized value thatrepresents a range of values for a parameter (such as parameter B). Eachbucket index can be thought of as an “index” corresponding to aparticular process window. Each bucket has process windows that overlapwith the process window of at least one adjacent bucket.

FIG. 7 is a chart showing the exemplary relationship between bucketnumbers and process windows for the buckets show in FIG. 6. Column 702represents the bucket number. Column 704 represents the lowerspecification limit (LSL). Column 706 represents the upper specificationlimit (USL). Column 708 represents the target value. As can be seen, thevalues in each bucket overlap with an adjacent bucket. For example,bucket 2 has a LSL of 2894.22 and a USL of 3078.23. Bucket 3 has a valueof 2978.43 and a USL of 3162.44. Therefore, there is an overlap betweenbucket 2 and bucket 3 in the range of 2978.43 and 3078.23. Anyobservations within that range will be counted in both bucket 2 andbucket 3.

Referring back to FIG. 6 again, the effect of using bucket values(represented by the bars, referred to generally as 604) instead ofnon-overlapping process window ranges (as shown in FIG. 5) is indicatedby a smoother response curve 602. The response curve shows a moreclearly defined peak (indicated as reference number 606) within theachievable process window.

While the present invention shows the use of generic parameters, e.g.parameter A, and parameter B. It is useful to consider some actualparameters used in performing this method for improving semiconductoryield. Parameters used may include, but are not limited to, the oxidethickness before contact lithography, the contact size afterlithographic development, the contact etch bias (contact size differencebefore and after etch), and the contact-to-poly alignment. Thecontact-to-poly alignment is a measure of how precisely positioned thecontacts are to polysilicon traces during fabrication. Due to machineerrors, contact positions on the wafer may be shifted relative topolysilicon (also referred to as “poly”). If contact positions have alot of variations due to poor alignment, some contacts may be shiftedvery close to poly and cause contact-to-poly shorts. While these areexamples of some parameters that are important in various semiconductorfabrication steps, other fabrication steps may have differentparameters. The present invention can be applied to many different typesof process parameters, beyond those listed above for the purposes ofexample.

FIG. 8 is a flowchart indicating process steps to perform an alternativeembodiment of the method of the present invention. In this embodiment,process steps 420-436 are identical to those described for FIG. 4. Inthe last process step 838, the optimized process windows areautomatically input to process tools to configure the process tools toutilize the optimized process windows. In this way, the results derivedfrom the present invention are automatically applied to a subsequentmanufacturing process.

The present invention may be implemented via software executing on oneor more computers. When multiple computers are used, they maycommunicate with each other via a communications network. FIG. 9 shows ablock diagram 900 of an exemplary system that implements the presentinvention. Data collection module 962 aggregates metrology data andinput data (see process steps 420-426). Regression module 964 performs aPartial Least Squares regression on data supplied by data collectionmodule 962 (see process step 428). Computation module computes optimalprocess windows, product limited yields, and predicted product yieldsbased on information supplied by regression module 964 (see processsteps 432-436). Report module 968 generates reports based on datasupplied by computation module 966 (see process step 438). The reportsmay include a tabular format, similar to that shown in FIG. 7.Additionally a graphical format, such as that shown in FIG. 6 may alsobe generated by report module 968. Optionally, tool configuration module970 configures one or more process tools based on data supplied bycomputation module 966 (see process step 838). These process tools mayinclude, but are not limited to, an etch tool, a polishing tool, alithography tool, and a deposition tool.

Although the invention has been shown and described with respect to acertain preferred embodiment or embodiments, certain equivalentalterations and modifications will occur to others skilled in the artupon the reading and understanding of this specification and the annexeddrawings. In particular regard to the various functions performed by theabove described components (assemblies, devices, circuits, etc.) theterms (including a reference to a “means”) used to describe suchcomponents are intended to correspond, unless otherwise indicated, toany component which performs the specified function of the describedcomponent (i.e., that is functionally equivalent), even though notstructurally equivalent to the disclosed structure which performs thefunction in the herein illustrated exemplary embodiments of theinvention. In addition, while a particular feature of the invention mayhave been disclosed with respect to only one of several embodiments,such feature may be combined with one or more features of the otherembodiments as may be desired and advantageous for any given orparticular application.

1. A method for optimizing multiple process windows, each process windowcorresponding to a different process parameter, in a semiconductormanufacturing process, comprising the steps of: performing dependentvariable composition on a plurality of dependent variables; retrievingmetrology data for each process parameter; joining the plurality ofdependent variables and the metrology data to form a joined data set;performing a partial least squares regression on the joined data set toobtain a prediction equation, and a variable importance prediction foreach process parameter; generating a process target value for eachparameter, based on the value of the corresponding variable importanceprediction; generating a new process window for each parameter, based onthe corresponding process target value, thereby forming a process windowset; evaluating the process window set by deriving a plurality ofproduct limited yield values based on data corresponding to the processwindow set, and comparing it to the plurality of product limited yieldvalues derived with a previous process window set, and computing apredicted product yield value based on the product of the plurality ofproduct limited yield values; and repeating the steps of generating aprocess target value for each parameter, based on the value of thecorresponding variable importance prediction and generating a newprocess target window for each parameter, based on the correspondingprocess target value until the predicted product yield value has reachedan optimal value, thereby deriving an optimized process window set. 2.The method of claim 1, further comprising the step of: generating areport displaying the process target value corresponding to each processwindow of the optimized process window set.
 3. The method of claim 2,further comprising the step of: generating a report displaying theprocess lower specification limit, and upper specification limitcorresponding to each process window of the optimized process windowset.
 4. The method of claim 1, further comprising the step of: inputtingthe optimized process window set to one or more process tools.
 5. Themethod of claim 1, wherein the step of evaluating the process window setby deriving a plurality of product limited yield values comprises:deriving a CA open product limited yield; and deriving a CA shortproduct limited yield.
 6. The method of claim 5, wherein the pluralityof dependent variables are selected from the group consisting of: oxidethickness before contact lithography; contact size after lithographicdevelopment; contact etch bias; and contact-to-polysilicon alignment. 7.The method of claim 5, wherein the step of performing dependent variablecomposition comprises the steps of: measuring a test structure yield foreach dependent variable on a plurality of semiconductor devices;calculating a lambda value based on the measured test structure yield;deriving a product limited yield for each dependent variable based onthe lambda value; and multiplying each product limited yield together toderive a predicted product yield.
 8. The method of claim 1, furthercomprising the steps of: generating a plurality of bucket indices,wherein each of the plurality of bucket indices corresponds to a processwindow, and each process window overlaps with the process window of atleast one adjacent bucket index; and wherein the step evaluating theprocess window set by deriving a process yield value based on datacorresponding to the process window set comprises inputting bucketobservation values into the prediction equation.
 9. The method of claim8, further comprising the step of: generating a yield response curvebased on the optimized process window set.
 10. The method of claim 8,wherein the step of generating a plurality of bucket indices comprisesthe step of: generating at least six bucket indices.
 11. The method ofclaim 8, wherein the step of generating a plurality of bucket indicescomprises: generating bucket indices corresponding to buckets comprisingprocess windows that overlap with the process window of at least oneadjacent bucket.
 12. A system for optimizing multiple process windows,comprising: a data collection module; a regression module; a computationmodule; and a report module, wherein the data collection module isconfigured to aggregate metrology data and input data, and communicatethe metrology data and input data to the regression module, theregression module is configured to perform a partial least squaresregression, and compute at least one variable importance prediction, anda prediction equation; the regression module further configured forcommunicating the at least one variable importance prediction, and theprediction equation to the computation module; the computation moduleconfigured for computing one or more optimized process windows, productlimited yields, and predicted product yields, the computation modulefurther configured for communicating the optimized process windows,product limited yields, and predicted product yields to the reportmodule; and the report module configured for outputting at least onereport.
 13. The system of claim 12, wherein: the report module isconfigured to output a report in a tabular format, the report indicatingvalues for a target value corresponding to each optimized processwindow.
 14. The system of claim 12, wherein: the report module isfurther configured to output a report indicating values for a lowerspecification limit, and an upper specification limit corresponding toeach optimized process window.
 15. The system of claim 12, wherein: thereport module is configured to output a report in a graphical format,the report comprising a yield response curve superimposed on a bar graphrepresentative of a distribution of observed values of a processparameter.
 16. The system of claim 12, wherein: the computation moduleis configured to generate a plurality of bucket indices, wherein each ofthe plurality of bucket indices corresponds to a process window, andeach process window overlaps with the process window of at least oneadjacent bucket index.
 17. The system of claim 12, further comprising: atool configuration module, wherein the tool configuration module isconfigured to receive process windows from the computation module, andwherein the tool configuration module is configured to communicateprocess windows to one or more process tools.
 18. The system of claim17, wherein the process tool comprises an etch tool.
 19. The system ofclaim 17, wherein the process tool comprises a deposition tool.
 20. Thesystem of claim 17, wherein the process tool comprises a lithographytool.